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I have found a 4271-digit 5-Carmichael number.
As far as I know, the previous record was 1015
digits by Chris Caldwell and Harvey Dubner.
The 5 prime factors are
12*413367181328934865310831672046650741477*5^707+1
24*413367181328934865310831672046650741477*5^707+1
36*413367181328934865310831672046650741477*5^707+1
72*413367181328934865310831672046650741477*5^707+1
(((48*413367181328934865310831672046650741477*5^707+3)^2-1)*\
((144*413367181328934865310831672046650741477*5^707+3)^2-1)/\
64-1)/7138+1
The first 4 were proven by Pfgw and
the last, with 2134 digits, by Primo.
David Broadhurst
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